SELECCIÓN DE PACIENTES

The model performance was evaluated using the following criteria:

• The NSE is a commonly used measure. Values for NSE vary from negative infinity to 1. A value of 1 indicates a perfect fit between observed and simulated data, while a value < 0 implies that the simulated value is (on average) a poorer predictor than the long-term average of the observations. The NSE criterion is often criticized due to the fact that the differences between the observed and simulated values are calculated as squared values. Thus, larger values are strongly over-estimated, while lower values are neglected (Legates and McCabe, 1999). This leads to an overestimation of model performance during peak flows and an underestimation during low flow conditions. A NSE of 0.4 – 0.6 is classified as satisfactory and a value > 0.6 is classified as good.

• The AVE provides the absolute difference between the observed and simulated value. Thus, a lower AVE is more desirable as opposed to a higher value.

• The coefficient of determination (r2) is defined as the squared value of the coefficient of correlation (Krause et al., 2005). It is also commonly defined as the squared ratio between the covariance and the multiplied standard deviations of the observed and simulated values (Krause, 2005). The coefficient of determination ranges between 0 (no correlation) and 1 (perfect fit). It should however be used with caution as a model which frequently over-or under-predicts may still exhibit an acceptable r2 value.

• The IOA (Willmott, 1981) aims to overcome the insensitivity of the NSE and r2 to differences in the observed and simulated means and variances (Legates and McCabe, 1999). The IOA, as with the NSE, is also very sensitive to peak flows and insensitive to low flows. The IOA ranges between 0-1, with a value of 0 representing no correlation and 1 a perfect fit. A value > 0.60 is regarded as representing a good fit between observed and simulated values.

The efficiency criteria of the water balance simulation for the calibration and validation periods are presented in Table 5-9. In terms of the model performance evaluation criteria, the model exhibits good results during the calibration period, i.e. a good correlation between the daily simulated and observed streamflow volumes were observed.

Table 5-9 Results of the Water Balance Simulation for the Calibration and Validation Periods

Performance Criteria 2009 2010 2009 and 2010 2011

NSE 0.58 0.22 0.55 negative

AVE (mm) 13.22 28.69 41.92 57.90

rsq 0.67 0.60 0.57 0.27

150 The effects of the use of different variations of rainfall stations on model results were also evaluated. Two configurations were considered, i.e. the exclusion of rainfall data recorded at De Hoek and Moorreesberg (Variation 1, Table 5-2) and only the use of rainfall data recorded inside the Sandspruit catchment (Zwavelberg, Oranjeskraal and Sandspruit; Variation 2; Table 5-2). The automatic calibration process was repeated to consider this variation in precipitation data. The results are presented in Table 5-10 and Table 5-11. The improvement in model performance, resulting from the omission of rainfall data recorded at De Hoek and Moorreesberg (Table 5-10) is clearly discernible. Thus it is not always appropriate to include all available data as the effect of orographic rainfall and the spatial variation of rainfall should be considered. The use of only rainfall data measured within the Sandspruit catchment resulted in further, although not significant, improvement in model performance. This improvement is not evident in the average, considering both 2009 and 2010, but rather in the increased stability of the performance evaluation criteria over 2009 and 2010.

Table 5-10 Results of the Water Balance Simulation for the Calibration and Validation Periods (Variation 1) Performance Criteria 2009 2010 2009 and 2010 2011 NSE 0.65 0.28 0.62 negative AVE (mm) 24.80 31.55 56.35 65.61 rsq 0.73 0.62 0.65 0.26 IOA 0.69 0.55 0.65 0.11

Table 5-11 Results of the Water Balance Simulation for the Calibration and Validation Periods (Variation 2) Performance Criteria 2009 2010 2009 and 2010 2011 NSE 0.62 0.51 0.61 negative AVE (mm) 24.80 22.72 47.52 63.52 rsq 0.66 0.63 0.64 0.27 IOA 0.69 0.61 0.67 0.11

Considering the results presented in Table 5-9, Table 5-10 and Table 5-11 it was decided to use the configuration producing results in Table 5-11, i.e. only utilizing rainfall data measured at Zwavelberg, Oranjeskraal and Sandspruit (Variation 2), for further analysis. The results of the automatic calibration process for this configuration are presented in Table 5-12. The model results discussed further, relate to that produced from Variation 2.

The observed and simulated streamflow are presented in Figure 5.16. During the calibration period, good correspondence between observed and simulated runoff was observed (Figure 5.16), in terms of temporal runoff dynamics. The model is able to represent the timing of initiation of increased runoff during winter. High peaks in the simulated runoff data set correspond well with that of the observed runoff and pronounced rainfall events (Figure 5.17). In general, the model under-estimated runoff volumes during extreme rainfall events.

The model was however not able to entirely replicate the ephemeral characteristic of the Sandspruit River, as baseflow was simulated during the summer months. This baseflow was generally in the order of 0.025 – 0.2 m3 s-1. The model also produced streamflow in response to pronounced rainfall events during summer, which is not evident in the observed streamflow data set.

151 The dominance of evapotranspiration, in terms of the catchment water balance was well replicated by the model as it amounted to more than 80% of the annual rainfall. This is in accordance with results presented by Bugan et al. (2012). During the main rainfall season, i.e. April to September, 67% (2009), 86% (2010) and 89% (2011) of the annual total simulated runoff was recorded. The rainfall season extended to November in 2009, during which 24% of the annual total simulated runoff occurred. The spatial distribution of rainfall, i.e. the average annual (2009 – 2011) rainfall per HRU, is illustrated in Figure 5.18. The model was able to accurately replicate the effects of topography and distance from the coastline on rainfall distribution (Figure 5.18).

The model was not able to accurately replicate the water balance of the Sandspruit catchment during the validation period. This creates uncertainty, in terms of the model’s ability to accurately replicate reality. This is often a result of calibrated parameter values, which are not necessarily physically relevant. However, the evidence provided in Figure 5.11, Figure 5.12 and Figure 5.14 also suggest that the observed streamflow data collected in 2011 contains errors. Operator inefficiency, equipment failure, changing rating tables or poor calibration of gauging weirs are all problems which are frequently encountered with streamflow records (Kienzle et al., 1997). Additionally, the variation in runoff dynamics observed in 2011 is not a result of variations in the temporal distribution of rainfall (Figure 5.9 and Table 5-3). Thus, it is uncertain whether the poor model performance during the validation period is a result of irrelevant model parameters/unsuitable model structure or due to errors in the observed runoff data set.

Table 5-12 Parameters Selected for Automatic Calibration (Variation 2)

Variable Definition

Values range in the calibration

Starting

value End value

a_rain

Maximum storage capacity of the interception storage per m2 of leaf area for rain

0 - 10 0.15 0.42

soilMaxDPS (mm) Maximum depression

storage capacity 0 - 10 3 5.25

soilPolRed

Polynomial reduction coefficient for the computation of actual ET

0 - 100 80 55.54

soilMaxInfWinter (mm) Maximum infiltration in the

winter half year 0 - 200 70 99.31

soilImpLT80

Relative infiltration capacity of areas with a sealed grade

< 80%

0 - 1 0.75 0.86

soilOutLPS Calibration coefficient for

outflow from the LPS 1 - 10 9 8.45

soilLatVertLPS

Calibration coefficient for allocation of LPS runoff to

lateral (interflow) and vertical (percolation)

components

0 - 10 10 7.96

soilMaxPerc (mm) Maximum percolation in the

time step 0 – 2000 14 1257.19

geoMaxPerc (mm)

Maximum percolation in the time step (into semi-

consolidated rock)

0 - 2000 2 481.10

soilConcRD1 Recession coefficient for

overland flow 0 - 10 10 9.53

soilConcRD2 Recession coefficient for

152 Variable Definition Values range in the calibration Starting

value End value

kdiff_layer Layer MPS diffusion factor 0 - 100 0.1 26.09

gwRG1RG2dist

Calibration coefficient for

water allocation to

percolation

0 - 1 1 0.73

gwRG1Fact Factor for runoff

contribution from RG1 0 – 10 2 0.78

gwRG2Fact Factor for runoff

contribution from RG2 0 - 10 4.5 3.51

gwCapRise Capillary rise coefficient 0 - 1 0.40 0.38

flowRouteTA Flood routing coefficient 0 - 100 10 1.25

cbWallhoehe Contour bank height (m) 0 - 1 0.64 0.62

The dominant component of simulated runoff was RD2 (Figure 5.18) which is interflow within the unsaturated zone. This is in accordance with observations made by Bugan et al. (2012) and Flügel (1995). In terms of proportion, this is followed by shallow groundwater flow (RG1). Minimal contributions from surface runoff (RD1) also occurred. Over the entire simulation period (2009 – 2011) the proportions of contribution to streamflow from the different components were:

• RD1 (surface runoff) – 6%

• RD2 (interflow within the unsaturated zone) – 70%

• RG1 (shallow groundwater flow) – 21%

• RG2 (baseflow) – 3% 0 1 2 3 4 5 6 7 8 9 10 01/2009 05/2009 09/2009 01/2010 05/2010 09/2010 01/2011 05/2011 09/2011 R u n o ff ( m 3/s ) Date

Runoff Plot

Observed Runoff Simulated Runoff

153 0 5 10 15 20 25 30 35 01/2009 05/2009 09/2009 01/2010 05/2010 09/2010 01/2011 05/2011 09/2011 P re ci p it a ti o n ( m m ) Date

Precipitation

Figure 5.17. Simulated catchment precipitation.

154 The simulated catchment runoff significantly increases during May. Rainfall and saturation of the soil initiates overland flow (RD1, Figure 5.19) and interflow (RD2, Figure 5.19) processes. The dominance of interflow (RD2) as a streamflow contributor is illustrated by its strong correlation with simulated runoff (Figure 5.16) and the catchment soil water storage dynamics (Figure 5.20). Recharge of the shallow perched and regional aquifer produces shallow groundwater flow, i.e RG1 (Figure 5.19). The contribution of RG1 to streamflow is particularly evident during the latter parts of the rainfall season. Simulated streamflow response during the dry summer months (Figure 5.16) is interpreted to be a result of persistent soil moisture during these months (Figure 5.20), particularly in the LPS. Observations by Bugan (2008) and Bugan et al. (2012) however suggest that these soil moisture reservoirs are depleted during the summer months. This discrepancy has also produced the pronounced AVE, as presented in Table 5-11.

0.0 0.5 1.0 1.5 2.0 2.5 01/2009 05/2009 09/2009 01/2010 05/2010 09/2010 01/2011 05/2011 09/2011 R u n o ff ( m m ) Date